WHAT IS A GAUGE TRANSFORMATION IN QUANTUM-MECHANICS

In classical theory, a physical state is an equivalence class under ga uge transformations. Is the same true in quantum theory? The physical quantum states are the solutions of Dirac's quantum constraint equatio n. They cannot be constructed as equivalence classes under the ''simpl e'' gauge transformations generated by the Dirac constraints. However, we show here that they can be constructed as equivalence classes unde r suitably defined ''complete'' gauge transformations. The complete ga uge transformations are generated by the action of the quantum constra ints on arbitrary individual components of the state.